Data-Driven Regularization Parameter Selection in Dynamic MRI

Abstract

In dynamic MRI, sufficient temporal resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based reconstructions. One problem in CS approaches is determining the regularization parameters, which control the balance between data fidelity and regularization. We propose a data-driven approach for the total variation regularization parameter selection, where reconstructions yield expected sparsity levels in the regularization domains. The expected sparsity levels are obtained from the measurement data for temporal regularization and from a reference image for spatial regularization. Two formulations are proposed. Simultaneous search for a parameter pair yielding expected sparsity in both domains (S-surface), and a sequential parameter selection using the S-curve method (Sequential S-curve). The approaches are evaluated using simulated and experimental DCE-MRI. In the simulated test case, both methods produce a parameter pair and reconstruction that is close to the root mean square error (RMSE) optimal pair and reconstruction. In the experimental test case, the methods produce almost equal parameter selection, and the reconstructions are of high perceived quality. Both methods lead to a highly feasible selection of the regularization parameters in both test cases while the sequential method is computationally more efficient.

Fast Compressed Sensing of 3D Radial T1 Mapping with Different Sparse and Low-Rank Models

“…This still ignores the problem of how to set the regularization parameters without a reference reconstruction, which remains an issue for most models. There are some methods that utilize automatic or data-driven regularization parameters, for example, with the wavelet regularization [ 39 ] and with TV regularization [ 40 ], but to our knowledge, no such methods exist for the models tested here in the qMRI setting.…”